Originally a switch-hitting infielder, Galan was in the minors from 1931 to 1933. He spent the latter two years with the San Francisco Seals and was teammates in 1933 with Joe DiMaggio and Vince DiMaggio, both of whom he out-hit with a .357 batting average (although they had higher slugging percentages). He broke into the majors in 1934 with the Chicago Cubs, primarily backing up Billy Herman at second base. He became the club's regular leftfielder the following summer, replacing Chuck Klein who moved to right when Babe Herman was traded away. That year, he hit .314 and paced the NL with 133 runs scored and 22 stolen bases as the Cubs won the pennant. He also went the entire season without grounding into a double play, although he did manage to hit into a triple play.

In 1936, Galan was selected to the All-Star team, and he became the first Cubs player to hit a home run in the Midsummer Classic. The following year, he swiped 23 bases, again leading the circuit. However, he missed much of the 1940 campaign after suffering a knee injury, and midway through the following season, he was dealt to the Brooklyn Dodgers.

Starting in 1943, Galan batted exclusively from the left side, but it did not seem to hurt him at the plate, as he hit over .300 with the Dodgers the next three seasons. After the 1946 season, he was traded to the Cincinnati Reds, for whom he hit .314 in his first season with the team.